Finite Group Databasebeta

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D3×C11×C13×D7 #26046559

order12012
automorphism?
homologyAbelianization (H1) = C22×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11×C13×D7
unambiguous semidirect product(D3×C7)⋊(C2×C11×C13)
unambiguous semidirect product(C3×D7)⋊(C2×C11×C13)
unambiguous semidirect productD21⋊(C2×C11×C13)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C22
derived, HallC3×C7 ⋊ C22×C11×C13
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C13 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C13
HallC7×C13 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×C13×D7
SylowC7 ⋊ C2×D3×C11×C13
SylowC3 ⋊ C2×C11×C13×D7

Subgroups

subgroupG/H
center, hypercenterC11×C13D3×D7
commutator, cosocle, hypocenterC3×C7C22×C11×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22
LCSG ▷ C3×C7
UCSC1 ◁ C11×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C13×D7×D9, D3×C11×C13×AGL(1,𝔽7), D3×C11×#10587720, …
maximal normal subgroup ofD3×C11×C13×AGL(1,𝔽7), D3×C11×#10587720, D3×C11×#10587721, …
maximal quotient ofC11×C13×D7×D9, C3×D3×C11×C13×D7, D3×C11×C13×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 149);